Method for Encoding Space-Time Codes in a Wireless Communication System Having Multiple Antennas

ABSTRACT

A method of transmitting space-time coded data in a wireless communication system having a plurality of antennas is disclosed. More specifically, the method includes allocating data symbols combined with complex weights to at least two transmit antennas during at least one specified time slot, and transmitting the data symbols combined with complex weights to a receiving end via the at least two transmit antennas during the at least one specified time slot.

TECHNICAL FIELD

The present invention relates to a method of encoding spaced time codesand more particularly, to a method of encoding space time codes in awireless communication system having multiple antennas.

BACKGROUND ART

With the widespread of telecommunication services coupled with theintroduction of various multimedia and high quality services, demandsfor communication services are increasing rapidly. In wirelesscommunication systems, frequency resources are limited and shared withother users. In order to actively respond to the demands, the capacityof the communication system plays an important role. As such, it isimportant to discover available frequency bandwidth and/or improveefficiency in using existing frequency resources. To address thislimited frequency resources problem, researches related to spatial-timedomain encoding are taking place to improve wireless resourceefficiency. For example, researches related to systems having multipleantennas both at the transmitting and the receiving sides are activelybeing researched so that communication reliability can be increasedusing existing resources through diversity gain and/or using paralleltransmissions to increase transmission capacity.

FIG. 1 illustrates a structural diagram of a communication device fortransmission/reception. More specifically in FIG. 1, the transmittingend includes a channel encoder 101, a mapper 102, a serial/parallel(S/P) converter 103, a multiple antenna encoder 104, and multipletransmit antennas 105.

The channel encoder 101 reduces noise effect by adding repeated bits(e.g., cyclic redundancy bits) to the data bits. The mapper 102 performsconstellation mapping where the data bits are allocated/mapped into datasymbols. The S/P converter 103 converts serially inputted data intoparallel data. The multiple antenna encoder 104 encodes the data symbolsinto time-space signals. The multiple antennas 105 transmit thetime-space encoded signals to a plurality of channels.

The receiving end includes multiple receiving antennas 106, a multipleantenna decoder 107, a parallel/serial (P/S) converter 108, a demapper109, and a channel decoder 110. The multiple receiving antennas 106receive signals via the plurality of channels. The multiple antennadecoder 107 decodes time-space signals encoded by the multiple antennaencoder 104 and converts the decoded signals into data symbols. Further,the P/S converter 108 converts the parallel symbols into serial symbols.The demapper 109 converts the serial data symbols to bits. Lastly, thechannel decoder decodes the channel codes processed through channelencoder 101 and then estimates the data.

As discussed above, the multiple antenna encoder 104 performs space-timecoding. Table 1 shows space-time codes derived from two or four transmitantennas.

TABLE 1 Number dp.min (minimum of Rank product distance) Scheme RateAntennas (Tx) (QPSK) (1) $\frac{1}{\sqrt{2}}\begin{bmatrix}S_{1} & {- S_{2}^{*}} \\S_{2} & S_{1}\end{bmatrix}$ 1 2 1 1 (2) $\frac{1}{\sqrt{2}}\begin{bmatrix}S_{1} \\S_{2}\end{bmatrix}$ 2 2 1 1 (3)${\frac{1}{\sqrt{2\left( {1 + r^{2}} \right)}}\begin{bmatrix}{S_{1} + {{jr} \cdot S_{4}}} & {{r \cdot S_{2}} + S_{3}} \\{S_{2} - {r \cdot S_{3}}} & {{{jr} \cdot S_{1}} + S_{4}}\end{bmatrix}},{r = {\sqrt{5} \pm \frac{1}{2}}}$ 2 2 2 0.2 (4)$\frac{1}{2}\begin{bmatrix}S_{1} & S_{2} & S_{3} & S_{4} \\S_{2}^{*} & {- S_{1}^{*}} & S_{4}^{*} & {- S_{3}^{*}} \\S_{3} & {- S_{4}} & {- S_{1}} & S_{2} \\S_{4}^{*} & S_{3}^{*} & {- S_{2}^{*}} & {- S_{1}^{*}}\end{bmatrix}$ 1 4 2 4 (5) $\frac{1}{\sqrt{2}}\begin{bmatrix}S_{1} & S_{2} & 0 & 0 \\{- S_{2}^{*}} & S_{1}^{*} & 0 & 0 \\0 & 0 & S_{3} & S_{4} \\0 & 0 & {- S_{3}^{*}} & S_{3}^{*}\end{bmatrix}$ 1 4 2 1 (6) $\frac{1}{2}\begin{bmatrix}S_{1} & {- S_{2}^{*}} & S_{5} & S_{6} \\S_{2}^{*} & S_{1}^{*} & S_{6} & S_{5}^{*} \\S_{3} & {- S_{4}^{*}} & S_{7} & {- S_{8}^{*}} \\S_{4} & S_{3}^{*} & S_{8} & S_{7}^{*}\end{bmatrix}$ 2 4 2 1

The space-time codes of Table 1, namely, (1), (2), and (3), arespace-time codes related to two (2) transmit antennas whereas (4), (5),and (6) are space-time codes related to four (4) transmit antennas.

The use of multiple antennas was proposed for the purposes of increasingcapacity, throughput, and/or coverage of the wireless communicationsystem. The multiple antennas are used to employ schemes such as aspatial division multiplexing (SDM or SM) and a space-time coding (STC).More specifically, the SM scheme sends different data to each of themultiple antennas so as to maximize the transmission rate. Further, theSTC scheme encodes the symbols across the spatial domain (e.g.,antennas) and the time domain to attain diversity gain as well as codinggain so as to increase link level capability. In addition, a generalizedform of the combination of SM and STC schemes is a linear dispersioncoding (LDC). The LDC matrix can be used in encoding/decoding operationsof the multiple antennas, and at the same time, in representing varioustechniques of the multiple antennas.

The multiple antenna encoding technique according to the LDC matrix canbe represented by the following equation.

$\begin{matrix}{S = {\sum\limits_{q = 1}^{Q}{S_{q}M_{q}}}} & \left\lbrack {{Equation}\mspace{14mu} 1} \right\rbrack\end{matrix}$

In Equation 1, Q denotes a number of data transmitted during a LDCinterval, T denotes the LDC interval, S_(q) denotes q^(th) transmissiondata and S_(q)=α_(q)+j*β_(q), M_(q) denotes is a dispersion matrix,having a size of T×N_(t), which is multiplied to the q^(th) transmissiondata, and S denotes a transmission matrix. Here, i^(th) column of the Stransmission matrix represents symbols that are transmitted during thei^(th) time period or time slot, and j^(th) row represents symbols thatare transmitted by the j^(th) antenna.

More generally, if each of an actual part (α_(q)) and an imaginary part(β_(q)) of S_(q) is spread across the space-time plane by differentdispersion matrix, this can be represented by Equation 2.

$\begin{matrix}{S = {\sum\limits_{q = 1}^{Q}\left( {{\alpha_{q}A_{q}} + {j\; \beta_{q}B_{q}}} \right)}} & \left\lbrack {{Equation}\mspace{14mu} 2} \right\rbrack\end{matrix}$

In Equation 2, A_(q) and B_(q) each denotes a dispersion matrix, havinga size of T×N_(t), which is respectively multiplied to the actual partand the imaginary part of S_(q).

If the data symbols are transmitted via the transmit antennas accordingto the scheme(s) as described above, the receiving signals received bythe receiving antennas can be expressed as follows. If the receivingsignals are multiplied to S_(q) by the same or identical LDC matrix,then it can be expressed according to the following equation.

$\begin{matrix}{\begin{bmatrix}Y_{1} \\\vdots \\Y_{Nr}\end{bmatrix} = {{H\; {\chi \begin{bmatrix}S_{1} \\\vdots \\S_{Q}\end{bmatrix}}} + \begin{bmatrix}n_{1} \\\vdots \\n_{Nr}\end{bmatrix}}} & \left\lbrack {{Equation}\mspace{14mu} 3} \right\rbrack\end{matrix}$

An equivalent channel response can be expressed by Equation 4 if theLDC, as shown in Equation 1, is applied.

H=I_(r){circle around (x)} H, X=[vec(M₀)vec(M₁) . . .vec(M)_(Q))]  [Equation 4]

In Equations 3 and 4, Nr denotes a number of receiving antennas, y_(Nr)denotes a signal value of the Nr^(th) receiving antenna, n_(Nr) denotesnoise from the Nr^(th) receiving antenna, H denotes the equivalentchannel response, and H denotes a channel response matrix having a sizeof N_(r)×N_(t).

If the receiving signal is applied the LDC of Equation 2, then thereceiving signal can be expressed as follows.

$\begin{matrix}{\begin{bmatrix}Y_{R,1} \\Y_{I,1} \\\vdots \\Y_{R,{Nr}} \\Y_{I,{Nr}}\end{bmatrix} = {{H\begin{bmatrix}\alpha_{1} \\\beta_{1} \\\vdots \\\alpha_{Q} \\\beta_{Q}\end{bmatrix}} + \begin{bmatrix}n_{R,1} \\n_{I,1} \\\vdots \\n_{R,{Nr}} \\n_{I,{Nr}}\end{bmatrix}}} & \left\lbrack {{Equation}\mspace{14mu} 5} \right\rbrack\end{matrix}$

In Equation 5, R (subscript) denotes the real part of the signal, and I(subscript) denotes the imaginary part of the signal. Here, theequivalent channel response can be expressed as shown in Equation 6.

$\begin{matrix}{{H\begin{bmatrix}{A_{1}{\underset{\_}{h}}_{1}} & {B_{1}{\underset{\_}{h}}_{1}} & \ldots & {{AQ}_{1}{\underset{\_}{h}}_{1}} & {B_{1}{\underset{\_}{h}}_{1}} \\\vdots & \vdots & \ddots & \vdots & \vdots \\{A_{1}{\underset{\_}{h}}_{Nr}} & {B_{1}{\underset{\_}{h}}_{Nr}} & \ldots & {A_{Q}{\underset{\_}{h}}_{Nr}} & {B_{Q}{\underset{\_}{h}}_{Nr}}\end{bmatrix}},{A_{q} = \begin{bmatrix}A_{R,q} & {- A_{I,q}} \\A_{I,q} & A_{R,q}\end{bmatrix}},{B_{q} = \begin{bmatrix}{- B_{I,q}} & {- B_{R,q}} \\B_{R,q} & {- B_{I,q}}\end{bmatrix}},{h_{n} = \begin{bmatrix}h_{R,n} \\h_{I,n}\end{bmatrix}}} & \left\lbrack {{Equation}\mspace{14mu} 6} \right\rbrack\end{matrix}$

In Equation 6, h_(R,n) denotes the real parts of the channel responsevector received via n^(th) receiving antenna, and h_(\I,n) denotes theimaginary parts of the channel response vector received via n^(th)receiving antenna. In other words, the multiple antenna decoding is aprocess by which transmitted signals are decoded using equations such asEquation 3 or Equation 5. To put differently, the multiple antennadecoding is a process of estimating S_(q) or α_(q) and β_(q).

In addressing capacity problems, a multiple input multiple output (MIMO)can be used increase transmission capacity of the wireless communicationsystem. Further, a space-time block coding, proposed by Alamouti, (ASimple Transmit Diversity Technique for Wireless Communications, IEEEJSAC, vol. 16, no. 8, October 1998) is an exemplary transmit diversitytechnique which uses a plurality of transmitting/receiving antennas toovercome fading in wireless channels. The Alamouti proposed scheme usestwo (2) transmit antennas, and the diversity order equals a product of anumber of transmit antennas and a number of receiving antennas. Here,the Alamouti proposed scheme transmits two (2) data symbols during two(2) time slots via two (2) transmit antennas, and as a result, atransmit rate (spatial multiplexing rate) is only 1. Consequently, thespatial multiplexing gain cannot be attained regardless how manyreceiving antennas are available. Here, the Alamouti proposed schemedoes not discuss the transmit techniques associated with three (3) ormore transmit antennas.

In addition, Bell Laboratories introduced another spatial multiplexingtechnique known as a vertical bell laboratories layered space-time(V-BLAST) system (Detection Algorithm and Initial Laboratory ResultsUsing V-BLAST Space-Time Communication Architecture, IEEE, Vol. 35, No.1, pp. 14-16, 1999). In this technique, each transmit antenna transmitsindependent signals simultaneously using the same transmit power andrate. At the receiving end, the transmitted signals are processedthrough detection ordering, interference nulling, and interferencecancellation procedures. By using the V-BLAST system, unnecessaryinterference signals can be eliminated or reduced thus increasing asignal-to-noise ratio (SNR). This technique is useful if the number ofreceiving antennas is equal or greater than the number of transmitantennas since independent data signals, corresponding to the number oftransmit antennas, can be simultaneously transmitted attaining a maximumspatial multiplexing gain. Here, a possible drawback is that there hasto be more receiving antennas than the transmit antennas. Moreover, ifthe channel condition is bad and thus the received signal isunsuccessfully decoded, detecting and decoding subsequent signal islikely to be affected as well affecting the system performance.

Further, different from the two techniques discussed above, Yao andWornwell (hereafter, “Yao”) proposed another spatial multiplexingtechnique called tilted-quadrature amplitude multiplexing (QAM)(Structured Space-Time Block Codes with Optimal Diversity-MultiplexingTradeoff and Minimum Delay, Globecom, pp. 1941-1945, 2003). Thistechnique is a full diversity and full rate (FDFR) STC which complementsan optimal diversity-multiplexing tradeoff proposed by Zheng and Tse.Yao's technique is used in a system having two (2) transmit antennas andtwo (2) receiving antennas where a short space-time block code has aminimum code length of 2. Further, the technique employs QAMconstellation rotation to attain spatial multiplexing gain as well asfull diversity gain. However, shortcomings with this technique is thatcoding gain is not fully realized since the rotation is a simplerotation of the signal, and the technique is applied and limited tosystems having two (2) transmit and receiving antennas, respectively.

DISCLOSURE OF THE INVENTION

Accordingly, the present invention is directed to a method of encodingspace-time codes in a wireless communication system having multipleantennas that substantially obviates one or more problems due tolimitations and disadvantages of the related art.

An object of the present invention is to provide a method oftransmitting space-time coded data in a wireless communication systemhaving a plurality of antennas.

Another object of the present invention is to provide an apparatus for atransmitting space-time coded data in a wireless communication systemhaving a plurality of antennas.

Additional advantages, objects, and features of the invention will beset forth in part in the description which follows and in part willbecome apparent to those having ordinary skill in the art uponexamination of the following or may be learned from practice of theinvention. The objectives and other advantages of the invention may berealized and attained by the structure particularly pointed out in thewritten description and claims hereof as well as the appended drawings.

To achieve these objects and other advantages and in accordance with thepurpose of the invention, as embodied and broadly described herein, amethod of transmitting space-time coded data in a wireless communicationsystem having a plurality of antennas includes allocating data symbolscombined with complex weights to at least two transmit antennas duringat least one specified time slot, and transmitting the data symbolscombined with complex weights to a receiving end via the at least twotransmit antennas during the at least one specified time slot.

In another aspect of the present invention, a method of transmittingspace-time coded data in a wireless communication system having aplurality of antennas includes allocating data symbols to at least twotransmit antennas during at least one specified time slot, andtransmitting the data symbols to a receiving end via the at least twotransmit antennas during the at least one specified time slot, whereinthe data symbols are combined with complex weights.

In a further aspect of the present invention, an apparatus fortransmitting space-time coded data in a wireless communication systemhaving a plurality of antennas includes a multiple antenna encoder forcombining complex weights with data symbols and allocating the datasymbols combined with complex weights to at least two transmit antennasduring at least one specified time slot, and a plurality of antennas fortransmitting the data symbols combined with complex weights to areceiving end via the at least two transmit antennas during the at leastone specified time slot.

It is to be understood that both the foregoing general description andthe following detailed description of the present invention areexemplary and explanatory and are intended to provide furtherexplanation of the invention as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are included to provide a furtherunderstanding of the invention and are incorporated in and constitute apart of this application, illustrate embodiment(s) of the invention andtogether with the description serve to explain the principle of theinvention. In the drawings;

FIG. 1 illustrates a structural diagram of a communication device fortransmission/reception;

FIG. 2 illustrates an example of an effect of a system having two (2)transmit antennas and one (1) receiving antenna using space-time coding;

FIG. 3 illustrates a performance comparison of a communication system,having two (2) transmit antennas and one (1) receiving antenna, usingSTC schemes;

FIG. 4 illustrates another performance comparison of a communicationsystem, having two (2) transmit antennas and one (1) receiving antenna,using STC schemes;

FIG. 5 illustrates a performance comparison between conventional STCschemes and the STC scheme according to the second embodiment; and

FIG. 6 illustrates subcarriers in an OFDM frequency domain.

BEST MODE FOR CARRYING OUT THE INVENTION

Reference will now be made in detail to the preferred embodiments of thepresent invention, examples of which are illustrated in the accompanyingdrawings. Wherever possible, the same reference numbers will be usedthroughout the drawings to refer to the same or like parts.

First Embodiment

In a first embodiment of the present invention, the wirelesscommunication system has two (2) transmit antennas. Encoding withspace-time code with respect to the first embodiment can transmit datasymbols in specified number of time slot units. In other words,space-time coding is applied in a specified number of time slots or timeslot units. The number of data symbols transmitted during the specifiedtime slots is determined by the number of transmit antennas available inthe system and/or by spatial multiplexing rate according to thespace-time coding.

More specifically, during the specified number of time slots,N_(t)(representing the number of transmit antennas)×R (spatialmultiplexing rate) number of data symbols (or a conjugate complex numberof the data symbol) and linearly combining weights or weight values fordata symbol transmission.

The weights or weight values can be linearly combined with the datasymbols. These weights or weight values can also be referred to ascomplex weights. Preferably, the weight values can change (or can beset) according to the transmit antenna(s) to be used for transmittingthe data symbols. In addition, it is possible to modify the firstembodiment to accommodate four (4) transmit antennas.

At this time, a discussion of space-time coding in a system having two(2) transmit antennas is presented. First, the spatial multiplexing ratecan be set to 1. Equation 7 shows a communication system having two (2)transmit antennas and a spatial multiplexing rate of 1. Here, thesignals represented on the same row(s) are transmitted by the sameantenna while the signals represented on the same column(s) aretransmitted during the same time slot. In other words, rows representantennas and the columns represent time. Referring to Equation 7, theantenna used for transmitting the signal located on the first row can bereferred to as Antenna #1, and the antenna used for transmitting thesignal located on the second row can be referred to as Antenna #2.

$\begin{matrix}{C_{New}^{2 \times 1} = \begin{bmatrix}{{w_{1}s_{1}} + {w_{2}s_{2}}} & {{{- w_{1}}s_{1}} + {w_{2}s_{2}}} \\{{w_{3}s_{1}^{*}} - {w_{4}s_{2}^{*}}} & {{w_{3}s_{1}^{*}} + {w_{4}s_{2}^{*}}}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 7} \right\rbrack\end{matrix}$

In the present application, an example of the space-time coding will beindicated as C_(New) ^(axb). Here, a denotes the number of transmitantennas, and b denotes the spatial time rate according to thespace-time coding.

In Equation 7, the data symbols are transmitted during two (2) timeslots or time slot units. That is, space-time coding is performed duringtwo (2) time slots. If performing space-time coding of the firstembodiment, that is, space-time coding is performed in a specifiednumber of time slots, the data symbols to be transmitted during thespecified number of time slots can be transmitted during each time slot,and weight values can be applied to the data symbols to be transmittedduring the specified number of time slots.

Referring to Equation 7, two (2) data symbols are transmitted during two(2) time slots. The data symbols s₁ and s₂ can be transmitted during thetwo (2) time slots. That is, s₁ and s₂ can all be transmitted duringeach time slot. Moreover, specified weights or weight values (w₁, w₂,w₃, w₄) can be applied to each data symbol s₁ and s₂. The details of theweights/weight values will be described below.

More specifically, the first transmit antenna (i.e., Antenna #1) cantransmit data symbols s₁ and s₂ during the first time slot, and to eachdata symbol, the weight values are applied. Moreover, the first transmitantenna (i.e., Antenna #1) can transmit data symbols s₁ and s₂ duringthe second time slot, and to each data symbol, weights are applied.Further, the second transmit antenna (i.e., Antenna #2) can transmitdata symbols s₁ and s₂, to each data symbol is applied weight values,during the first time slot, and can transmit data symbols s₁ and s₂, toeach data symbol is applied weight values, during the second time slot.The weight values can vary from one time slot to another time slot aswell as from one transmit antenna to another transmit antenna. Further,a total power of the transmit antennas during a same time slot is thesame.

In the space-time coding scheme according to the first embodiment, anentire set of data symbols to be transmitted during a specified timeslot can be transmitted during a single time slot. Further, weights orweight values are applied to all of the data symbols transmitted duringthe single time slot. Preferably, a result of linearly combinedspecified weight vector and the data symbol is transmitted during thesingle time slot.

The weights or weight values can be expressed as shown in Equation 8.

$\begin{matrix}{{w_{1} = \frac{^{{j\theta}_{a}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},{w_{2} = \frac{r\; ^{{j\theta}_{b}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},{w_{3} = \frac{r\; ^{{j\theta}_{c}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},{w_{4} = \frac{^{{j\theta}_{d}}}{\sqrt{2\left( {1 + r^{2}} \right)}}}} & \left\lbrack {{Equation}\mspace{14mu} 8} \right\rbrack\end{matrix}$

Equation 8 is an equation used to describe the weight values used inEquation 7. As such, the weight values can be constructed in differentform and not limited to Equation 8. That is, the weight values ofEquation 7 can be complex number(s) having different values, and notlimited to Equation 8.

The weight values (w₁, w₂, w₃, w₄) can be determined using phase values(θ_(a), θ_(b), θ_(c), θ_(d)) and a real number r. These variable numberscan be of different values. In other words, the variable numbers canhave a different optimal value based on the system, and if thetransmitting/receiving end lacks the channel information, the variablenumber can have optimum capability by satisfying Equation 9.

θ_(a)+θ_(b)=θ_(c)+θ_(d), r=1  [Equation 9]

Preferably, each of the weight values applied in Equation 7 have thesame amplitude, and the sum of the phase of any two (2) weight values issame as the sum of the phase of the remaining two (2) weight values. IfEquation 9 is satisfied, then a minimum product distance (indicated as‘dp.min’ in Table 1) with respect to Equation 7 can be optimized.

Equation 10 is an example of space-time coding according to the firstembodiment which satisfies the conditions of Equation 9.

$\begin{matrix}{C_{New}^{2 \times 1} = {\frac{1}{\sqrt{4}}\begin{bmatrix}{s_{1} + s_{2}} & {{- s_{1}} + s_{2}} \\{s_{1}^{*} - s_{2}^{*}} & {s_{1}^{*} + s_{2}^{*}}\end{bmatrix}}} & \left\lbrack {{Equation}\mspace{14mu} 10} \right\rbrack\end{matrix}$

FIG. 2 illustrates an example of an effect of a system having two (2)transmit antennas and one (1) receiving antenna using space-time coding.In FIG. 2, the space-time coding (STC) scheme of Equation 7 and Alamouticoding scheme (space-time coding scheme (1) of Table 1) are compared. Ifthe data symbols are uncoded (e.g., channel encoding is not applied orturbo-coded, the STC scheme of Equation 7 shows the same optimal resultas that of the Alamouti scheme. The Alamouti coding, as described abovewith respect to Table 1, provides only one coding method. However, theSTC scheme of Equation 7 can use different values for each parameter ofEquation 8. That is, each parameter of Equation 8 can have differentvalues to provide various types of space-time coding according to thefeatures/capabilities of different communication systems. As such, theSTC scheme of can have better performance than the Alamouti codingscheme in certain communication environments.

In the embodiment of the present invention, the multiple data symbolsare transmitted using two or more transmit antennas. Further, each datasymbol can be modulated and encoded according to a modulation and codingset (MCS) level, for example. The MCS level can be fed back from thereceiving end or alternatively, can be determined at the transmittingend.

As discussed, a full diversity gain can be attained using the space-timecoding of Equation 7. More specifically, if the diversity order is 4,each data symbol space-time coded according to Equation 7 can achievemaximum diversity gain. In other words, the STC of Equation 7 providesequal or similar amount of diversity to each data symbol. Preferably,the data symbols are allocated the same MCS level. Preferably, each datasymbol transmitted according to the STC of Equation 7 are applied thesame modulation method (e.g., all data symbols mapped using 16 QAM) andthe same coding method (e.g., channel coding using the same codingrate).

At this time, another example in a communication system having two (2)transmit antennas according to the first embodiment of the presentinvention will be explained. Here, the first embodiment is applied tothe two (2) antenna system with the spatial multiplexing rate of 2. InEquation 11 below, the antenna used to transmit the signal located inthe first row is referred to as Antenna #1. Similarly, the antenna usedto transmit the signal in the second row is referred to as Antenna #2.

$\begin{matrix}{C_{New}^{2 \times 2} = {\frac{1}{\sqrt{4}}\begin{bmatrix}{{w_{1}s_{1}} + {w_{2}s_{2}} + {w_{3}s_{3}} + {w_{4}s_{4}}} & {{{- w_{1}}s_{1}} - {w_{2}s_{2}} + {w_{3}s_{3}} + {w_{4}s_{4}}} \\{{w_{5}s_{1}} + {w_{6}s_{2}} - {w_{7}s_{3}} - {w_{8}s_{4}}} & {{w_{5}s_{1}} + {w_{6}s_{2}} + {w_{7}s_{3}} + {w_{8}s_{4}}}\end{bmatrix}}} & \left\lbrack {{Equation}\mspace{14mu} 11} \right\rbrack\end{matrix}$

Referring to Equation 11, the data symbols are transmitted in two (2)time slots. In other words, the data symbols are space-time coded duringthe two (2) time slots. If the data symbols are space-time coded duringa specified number of time slots according to the first embodiment, allof the data symbols to be transmitted during the specified number oftime slots can be transmitted during each time slot, and weight valuescan be applied to these data symbols.

In Equation 11, four (4) data symbols are transmitted during two (2)time slots. More specifically, the data symbols, s₁, s₂, s₃, s₄, aretransmitted during two (2) time slots, and during each time slot, all ofthe data symbols, s₁, s₂, s₃, s₄, are transmitted. Further, weightvalues, w₁, w₂, w₃, w₄, w₅, w₆, w₇, w₈, are applied to the data symbols,s₁, s₂, s₃, s₄.

During the first time slot, the data symbols, s₁, s₂, s₃, s₄, aretransmitted with weight values applied thereto from Antenna #1.Similarly, the data symbols, s₁, s₂, s₃, s₄, with weight values appliedthereto are transmitted via Antenna #2 during the first time slot.During the second time slot, the data symbols, s₁, s₂, s₃, s₄, aretransmitted with weight values applied thereto from each of Antenna #1and Antenna #2. The weight values can change or vary based on the timeslot and/or each transmit antenna.

As discussed, the STC scheme according to the first embodiment transmitsall of the data symbols, which are scheduled to be transmitted during aspecified number of time slots, during each time slot. Moreover, weightvalues are applied to all of the data symbols transmitted during eachtime slot. Preferably, the result of linearly combined specified weightvector and the data symbol is transmitted during the single time slot.

Equation 12 shows the weight values related to Equation 11.

$\begin{matrix}{{{w_{1} = \frac{^{j\; \theta_{a}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{2} = \frac{r\; ^{j\; \theta_{b}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{3} = \frac{^{j\; \theta_{c}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{4} = \frac{r\; ^{j\; \theta_{d}}}{\sqrt{4\left( {1 + r^{2}} \right)}}}}{{w_{5} = \frac{r\; ^{j\; \theta_{e}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{6} = \frac{^{j\; \theta_{f}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{7} = \frac{r\; ^{j\; \theta_{g}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{8} = \frac{^{j\; \theta_{h}}}{\sqrt{4\left( {1 + r^{2}} \right)}}}}} & \left\lbrack {{Equation}\mspace{14mu} 12} \right\rbrack\end{matrix}$

Here, Equation 12 is an equation used to describe the weight values usedin Equation 11. As such, the weight values can be constructed indifferent form and not limited to Equation 12. That is, the weightvalues of Equation 11 can be complex number(s) having different values,and not limited to Equation 12.

Referring to the weight values of Equation 12, w₁, w₂, w₃, w₄, w₇, w₈are pure real numbers, w₅, w₆ are pure imaginary numbers, and r timesthe specified amplitude exists between w₁, w₃, w₆, w₈, and w₂, w₄, w₅,w₇. Here, r can be

$\frac{\sqrt{5} + 1}{2}\mspace{14mu} {or}\mspace{14mu} {\frac{\sqrt{5} - 1}{2}.}$

As discussed above with respect to the MCS level, a full diversity gaincan be attained using the space-time coding of Equation 11. Morespecifically, if the diversity order is 4, each data symbol space-timecoded according to Equation 11 can achieve maximum diversity gain. Inother words, the STC of Equation 11 provides equal or similar amount ofdiversity to each data symbol. Preferably, the data symbols areallocated the same MCS level. Preferably, each data symbol transmittedaccording to the STC of Equation 11 are applied the same modulationmethod (e.g., all data symbols mapped using 16 QAM) and the same codingmethod (e.g., channel coding using the same coding rate).

FIG. 3 and FIG. 4 illustrate a performance comparison of a communicationsystem, having two (2) transmit antennas and one (1) receiving antenna,using STC schemes. The graph of FIG. 3 shows the performance of the4-QAM constellation mapping scheme without STC. The graph of FIG. 4shows the performance of the 4-QAM constellation mapping scheme withturbo-coding.

More specifically, FIG. 3 is a result of comparing the spatialmultiplexing (SM) scheme (2) of Table 1, a generalized optimal diversity(GOD) scheme (3) of Table 1, and space-time coding (STC) scheme ofEquation 11. The STC scheme of Equation 11 uses two (2) transmitantennas with the SM rate of 2. Here, the STC scheme (2) of Table 1 andthe GOD scheme (3) of Table 1 are used to show the performance ofEquation 11. As illustrated, if the STC is not used, the STC of Equation11 shows better performance than the SM coding while showing similar toequal performance to the GOD coding.

FIG. 4 illustrates a comparison of the GOD scheme between scheme (3) ofTable 1 and STD scheme of Equation 11. As shown in FIG. 3, the twoschemes showed same performance result even when no channel coding wasused. However, when turbo coding was used for channel coding, the STCscheme of Equation 11 showed better performance. Further, turbo code forspace-time coding according to Equation 11 showed better performancethan the GOD coding scheme as well.

In summary, the STC according to the first embodiment showed equalperformance in certain situations. However, the STC according to thefirst embodiment is able to manipulate the weight values applied to thedata symbols. As discussed by referring to FIGS. 2-4, differentcharacteristics can be expressed based on the channel condition even ifthe STC is the same. The STC according to the embodiment of the presentinvention can have better performance than the conventional STC incertain situations.

Second Embodiment

In a second embodiment of the present invention, the space-time codingcan be applied in a communication system having four (4) transmitantennas. Here, the STC scheme can be represented by the data symbolsbeing transmitted during a specified number of time slots. Further,weight values are applied to each data symbol (or to the conjugatecomplex number of the data symbol) before being transmitted to thereceiving end. The weight values applied to the data symbols arepreferably changed or modified based on the antenna which is used totransmit the data symbols. Moreover, the weight values are preferablychanged or modified based on the time slots which are used to transmitthe weight-applied data symbol.

The discussion of the second embodiment is based on the wirelesscommunication system having four (4) antennas which is an expandedmodification from the first embodiment.

$\begin{matrix}{C_{{New}\; 1}^{4 \times 1} = \begin{bmatrix}{{w_{1}s_{1}} + {w_{2}s_{2}}} & {{{- w_{1}}s_{1}} + {w_{2}s_{2}}} & 0 & 0 \\{{w_{3}s_{1}^{*}} - {w_{4}s_{2}^{*}}} & {{w_{3}s_{1}^{*}} + {w_{4}s_{2}^{*}}} & 0 & 0 \\0 & 0 & {{w_{1}s_{3}} + {w_{2}s_{4}}} & {{{- w_{1}}s_{3}} + {w_{2}s_{4}}} \\0 & 0 & {{w_{3}s_{3}^{*}} - {w_{4}s_{4}^{*}}} & {{w_{3}s_{3}^{*}} + {w_{4}s_{4}^{*}}}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 14} \right\rbrack\end{matrix}$

Equation 14 shows the STC scheme of a communication system having four(4) antennas and the spatial multiplexing rate of 1. Here, the signalslocated on the same row(s) are transmitted by the same antenna while thesignals located on the same column(s) are transmitted during the sametime slot. In other words, rows represent antennas and the columnsrepresent time. Referring to Equation 14, the antenna used fortransmitting the signal located on the first row can be referred to asAntenna #1, the antenna used for transmitting the signal located on thesecond row can be referred to as Antenna #2, the antenna used fortransmitting the signal located on the third row can be referred to asAntenna #3, and the antenna used for transmitting the signal located onthe fourth row can be referred to as Antenna #4.

Referring to Equation 14, the data symbols are transmitted during four(4) time slots. In the space-time coding according to the secondembodiment, if the space-time coding is performed using a specifiednumber of time slots, each transmit antenna transmits a specific datasymbol, all of the data symbols to be transmitted via the specifiedantennas are transmitted during the specified number of time slots, andweight values are applied to the data symbols transmitted during thespecified number of time slots.

Referring to Equation 14, four (4) transmit antennas transmit four (4)data symbols, s₁, s₂, s₃, s₄, during four (4) time slots. Further, eachtransmit antenna transmits two (2) data symbols during four (4) timeslots. The data symbols, s₁ and s₂, are transmitted via Antenna #1 andAntenna #2, respectively, during the first two (2) time slots of thefour (4) time slots. Moreover, the weight values, w₁, w₂, w₃, w₄, areapplied to each data symbol, s₁ and s₂. Furthermore, the data symbols,s₃ and s₄, are transmitted via Antenna #3 and Antenna 4, respectively,during the third and four time slots. Similarly, the weight values, w₁,w₂, w₃, w₄, are applied to each data symbol, s₃ and s₄. As discussedabove, the weight values applied to data symbols can vary/change fromone time slot to another, and also from one antenna to another.

The weights or weight values as shown in Equation 14 can be expressedaccording to Equation 15.

$\begin{matrix}{{w_{1} = \frac{^{j\; \theta_{a}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},\mspace{14mu} {w_{2} = \frac{r\; ^{j\; \theta_{b}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},{w_{3} = \frac{r\; ^{j\; \theta_{c}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},\mspace{14mu} {w_{4} = \frac{^{j\; \theta_{d}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},} & \left\lbrack {{Equation}\mspace{14mu} 15} \right\rbrack\end{matrix}$

Equation 15 is an equation used to describe the weight values used inEquation 14. As such, the weight values can be constructed in differentform and not limited to Equation 14. That is, the weight values ofEquation 15 can be complex number(s) having different values, and notlimited to Equation 15.

The weight values (w₁, w₂, w₃, w₄) can be determined using phase values(θ_(a), θ_(b), θ_(c), θ_(d)) and a real number r. These variable numberscan be of different values. In other words, the variable numbers canhave a different optimal value based on the system, and if thetransmitting/receiving end lacks the channel information, the variablenumber can have optimum capability by satisfying Equation 16.

θ_(a)+θ_(b)=θ_(c)+θ_(d), r=1  [Equation 16]

Preferably, each of the weight values applied in Equation 14 have thesame amplitude, and the sum of the phase of any two (2) weight values issame as the sum of the phase of the remaining two (2) weight values. IfEquation 16 is satisfied, then a minimum product distance (indicated as‘dp.min’ in Table 1) with respect to Equation 7 can be optimized.

The STC scheme of Equation 14 corresponds to the STC scheme indicated by(5) of Table 1. Here, the STC scheme of Equation 14 shows similar toequal effectiveness to that of scheme (5) of Table 1. Further, the STCscheme of Equation 14 can be used to manipulate the weight values toprovide various STC combinations for further effectiveness.

Looking at the signal transmitted via Antenna #1, for example, the datasymbols, s₁ and s₂, are transmitted after being combined. Similarly, thedata symbols, s₁ and s₂, transmitted via Antenna #2 are also combinedbefore transmission. Further, the data symbols, s₃ and s₄, are combinedand transmitted via Antenna #3 and Antenna #4, respectively.

The data symbols, s₁ and s₂, are transmitted via the same channel (i.e.,first channel) while the data symbols, s₃ and s₄, are transmitted viathe same channel (i.e., second channel). Here, the same MCS level can beapplied to the data symbols transmitted during the same specified timeslot. That is, a first MCS level is assigned to the data symbols, s₁ ands₂, and a second MCS level is assigned to the data symbols, s₃ and s₄.The first MCS level and the second MCS level can be same or different.

If the space-time coding, which does not provide full diversity, isused, it is preferable to assign the same level MCS level to theweight-combined data symbols which are transmitted during a specifictime slot.

The following is another example of space-time coding in a four (4)antenna system in which the space multiplexing rate is 1.

$\begin{matrix}{C_{{New}\; 2}^{4 \times 1} = \begin{bmatrix}{{w_{1}{\overset{\sim}{x}}_{1}} + {w_{2}{\overset{\sim}{x}}_{2}}} & {{{- w_{1}}{\overset{\sim}{x}}_{1}} + {w_{2}{\overset{\sim}{x}}_{2}}} & 0 & 0 \\{{w_{3}{\overset{\sim}{x}}_{1}^{*}} - {w_{4}{\overset{\sim}{x}}_{2}^{*}}} & {{w_{3}{\overset{\sim}{x}}_{1}^{*}} + {w_{4}{\overset{\sim}{x}}_{2}^{*}}} & 0 & 0 \\0 & 0 & {{w_{1}{\overset{\sim}{x}}_{3}} + {w_{2}{\overset{\sim}{x}}_{4}}} & {{{- w_{1}}{\overset{\sim}{x}}_{3}} + {w_{2}{\overset{\sim}{x}}_{4}}} \\0 & 0 & {{w_{3}{\overset{\sim}{x}}_{3}^{*}} - {w_{4}{\overset{\sim}{x}}_{4}^{*}}} & {{w_{3}{\overset{\sim}{x}}_{3}^{*}} + {w_{4}{\overset{\sim}{x}}_{4}^{*}}}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 17} \right\rbrack\end{matrix}$

In Equation 17, the data symbols are transmitted during four (4) timeslots. That is, the space-time coding is performed during four (4) timeslots. Referring to Equation 17, x_(i)=s_(i)e^(jθ) ^(r) , where i=1, 2,3, 4, and {tilde over (x)}₁=x₁ ^(R)+jx₃ ^(I), {tilde over (x)}₂=x₂^(R)+jx₄ ^(I), {tilde over (x)}₃=x₃ ^(R)+R+jx₁ ^(I), and {tilde over(x)}₄=x₄ ^(R)+jx₂ ^(I). Here, the superscript R represents a real numberof a complex number, and I represents an imaginary number of a complexnumber.

Further, all four (4) antennas transmit signals {tilde over (x)}₁,{tilde over (x)}₂, {tilde over (x)}₃, {tilde over (x)}₄ which correspondto data symbols s₁, s₂, s₃, s₄ during four (4) time slots. In addition,since the signals {tilde over (x)}₁, {tilde over (x)}₂, {tilde over(x)}₃, {tilde over (x)}₄ are derived from each of the data symbols, s₁,s₂, s₃, s₄, each transmit antenna transmits signals which correspond todata symbols s₁, s₂, s₃, s₄ during the four (4) time slots. Morespecifically, {tilde over (x)}₁ and {tilde over (x)}₂ corresponding tothe data symbols s₁, s₂, s₃, s₄ are transmitted via Antenna #1 andAntenna #2, respectively, the signals are transmitted during the firsttwo time slots out of four (4) time slots, and specific weight valuesw₁, w₂, w₃, w₄ are applied. Furthermore, {tilde over (x)}₃ and {tildeover (x)}₄ corresponding to the data symbols s₁, s₂, s₃, s₄ aretransmitted via Antenna #3 and Antenna #4, respectively, the signals aretransmitted during the last two time slots out of four (4) time slots,and specific weight values w₁, w₂, w₃, w₄ are applied.

In other words, Antenna #1 and Antenna #2 can be used to transmit {tildeover (x)}₁ and {tilde over (x)}₂ corresponding to the data symbols s₁,s₂, s₃, s₄, respectively, and Antenna #3 and Antenna #4 can be used totransmit {tilde over (x)}₃ and {tilde over (x)}₄ corresponding to thedata symbols s₁, s₂, s₃, s₄, respectively. The weight values applied tothe signals, {tilde over (x)}₁, {tilde over (x)}₂, {tilde over (x)}₃,{tilde over (x)}₄, or the weight values applied to the data symbols, s₁,s₂, s₃, s₄, can vary from one time slot to another and can also varyfrom one transmit antenna to another.

The weights or weight values can be expressed as shown in Equation 18.

$\begin{matrix}{{w_{1} = \frac{^{j\; \theta_{a}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},\mspace{14mu} {w_{2} = \frac{r\; ^{j\; \theta_{b}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},{w_{3} = \frac{r\; ^{j\; \theta_{c}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},\mspace{14mu} {w_{4} = \frac{^{j\; \theta_{d}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},} & \left\lbrack {{Equation}\mspace{14mu} 18} \right\rbrack\end{matrix}$

Equation 18 is an equation used to describe the weight values used inEquation 17. As such, the weight values can be constructed in differentform and not limited to Equation 18. That is, the weight values ofEquation 17 can be complex number(s) having different values, and notlimited to Equation 18.

The weight values (w₁, w₂, w₃, w₄) can be determined using phase values(θ_(a), θ_(b), θ_(c), θ_(d)) and a real number r. These variable numberscan be of different values. In other words, the variable numbers canhave a different optimal value based on the system, and if thetransmitting/receiving end lacks the channel information, the variablenumber can have optimum capability by satisfying Equation 19 andEquation 20.

θ_(a)+θ_(b)=θ_(c)+θ_(d), r=1  [Equation 19]

Preferably, each of the weight values applied in Equation 18 have thesame amplitude, and the sum of the phase of any two (2) weight values issame as the sum of the phase of the remaining two (2) weight values.

[Equation  20] $\begin{matrix}{\theta_{r} = {\frac{1}{2}\tan^{- 1}}} & (2)\end{matrix}$

θ_(r) can be used to determine x_(i) and s_(i).

The STC of Equation 17 can be used to improve the STC of Equation 14.the STC of Equation 17 has a rank of 4, and a minimum product distanceof 0.25. The rank corresponds to diversity gain based on space-timecoding, and the minimum product distance corresponds to coding gain.

As discussed, full diversity gain can be attained by the STC schemeaccording to Equation 17. A same MCS level is preferably assigned to thedata symbols transmitted according to the STC scheme of Equation 17. Inother words, the same MCS level is applied to each data symboltransmitted according to the STC scheme of Equation 17.

The following is another example of space-time coding that can beapplied to a four (4) antenna system in which the spatial multiplexingrate is 1.

$\begin{matrix}{C_{{New}\; 3}^{4 \times 1} = \begin{bmatrix}\begin{matrix}{{w_{1}s_{1}} + {w_{2}s_{2}} +} \\{{w_{3}s_{3}} + {w_{4}s_{4}}}\end{matrix} & \begin{matrix}{{{- w_{1}}s_{1}} - {w_{2}s_{3}} +} \\{{w_{3}s_{3}} + {w_{4}s_{4}}}\end{matrix} & 0 & 0 \\\begin{matrix}{{w_{5}s_{1}} + {w_{6}s_{2}} -} \\{{w_{7}s_{3}} - {w_{8}s_{4}}}\end{matrix} & \begin{matrix}{{w_{5}s_{1}} + {w_{6}s_{2}} +} \\{{w_{7}s_{3}} + {w_{8}s_{4}}}\end{matrix} & 0 & 0 \\0 & 0 & \begin{matrix}{{w_{1}s_{1}} + {w_{2}s_{2}} +} \\{{w_{3}s_{3}} + {w_{4}w_{4}}}\end{matrix} & \begin{matrix}{{{- w_{1}}s_{1}} - {w_{2}s_{2}} +} \\{{w_{3}s_{3}} + {w_{4}s_{4}}}\end{matrix} \\0 & 0 & \begin{matrix}{{w_{5}s_{1}} + {w_{6}s_{2}} -} \\{{w_{7}s_{3}} - {w_{8}s_{4}}}\end{matrix} & \begin{matrix}{{w_{5}s_{1}} + {w_{6}s_{2}} +} \\{{w_{7}s_{3}} + {w_{8}s_{4}}}\end{matrix}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 21} \right\rbrack\end{matrix}$

In Equation 21, the data symbols are transmitted during four (4) timeslots. That is, the space-time coding is performed during four (4) timeslots.

In Equation 21, four (4) data symbols are transmitted via four (4)antennas during four (4) time slots. In other words, each transmitantenna transmits four (4) data symbols during four (4) time slots. Ifdata symbols, s₁, s₂, s₃, s₄, are transmitted via Antenna #1 and Antenna#2, these data symbols are transmitted during the first two (2) out offour (4) time slots, and the weight values, w₁, w₂, w₃, w₄, are appliedto each data symbol. Further, if data symbols, s₁, s₂, s₃, s₄, aretransmitted via Antenna #3 and Antenna #4, these data symbols aretransmitted during the last two (2) out of four (4) time slots, and theweight values, w₅, w₆, w₇, w₈, are applied to each data symbol.

The each antenna according to the second embodiment can be used totransmit specific data symbol. At the same time, all transmit antennascan be used to transmit the data symbols, s₁, s₂, s₃, s₄. Further, theweight values applied to the data symbols, s₁, s₂, s₃, s₄, can vary fromone time slot to another as well as from one antenna to another.

Equation 22 shows the weight values related to Equation 21.

$\begin{matrix}{{w_{1} = \frac{^{j\; \theta_{a}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},\mspace{14mu} {w_{2} = \frac{r\; ^{j\; \theta_{b}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{3} = \frac{\; ^{j\; \theta_{c}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},\mspace{14mu} {w_{4} = \frac{r\; ^{j\; \theta_{d}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{5} = \frac{r\; ^{j\; \theta_{e}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},\mspace{14mu} {w_{6} = \frac{\; ^{j\; \theta_{f}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{7} = \frac{r\mspace{11mu} ^{j\; \theta_{g}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},\mspace{14mu} {w_{8} = \frac{\; ^{j\; \theta_{h}}}{\sqrt{4\left( {1 + r^{2}} \right)}}}} & \left\lbrack {{Equation}\mspace{14mu} 22} \right\rbrack\end{matrix}$

Here, Equation 22 is an equation used to describe the weight values usedin Equation 21. As such, the weight values can be constructed indifferent form and not limited to Equation 22. That is, the weightvalues of Equation 21 can be complex number(s) having different values,and not limited to Equation 22.

Referring to the weight values of Equation 22, w₁, w₂, w₃, w₄, w₇, w₈are determined by phase values, θ_(a), θ_(b), θ_(c), θ_(d), θ_(e),θ_(f), θ_(g), θ_(h), and a real number, r. As such, these variablenumbers can be of different values. In other words, the variable numberscan have a different optimal value based on the system, and if thetransmitting/receiving end lacks the channel information, the variablenumber can have optimum capability by satisfying Equation 23.

$\begin{matrix}{{r = \frac{\sqrt{5} \pm 1}{2}},\mspace{14mu} {\theta_{a} = {\theta_{b} = {\theta_{c} = {\theta_{d} = 0}}}},{\theta_{e} = \frac{3\; \pi}{2}},\mspace{14mu} {\theta_{f} = \frac{\pi}{2}},\mspace{14mu} {\theta_{g} = \pi},\mspace{14mu} {\theta_{h} = 0}} & \left\lbrack {{Equation}\mspace{14mu} 23} \right\rbrack\end{matrix}$

That is, referring to Equation 23, preferably, w₁, w₂, w₃, w₄, w₇, w₈are real numbers, w₅, w₆ are imaginary numbers, and r times thespecified amplitude exists between w₁, w₃, w₆, w₈ and w₂, w₄, w₅, w₇.Here, r can be

$\frac{\sqrt{5} + 1}{2}\mspace{14mu} {or}\mspace{14mu} {\frac{\sqrt{5} - 1}{2}.}$

As discussed above with respect to the MCS level, a full diversity gaincan be attained using the space-time coding of Equation 21. Preferably,the data symbols, which are transmitted according to the STC of Equation21, are allocated the same MCS level. Preferably, each data symboltransmitted according to the STC of Equation 21 are applied the samemodulation method and the same coding method.

FIG. 5 illustrates a performance comparison between conventional STCschemes and the STC scheme according to the second embodiment. Theresult of FIG. 5 is based on using turbo coding for space-time coding,and if 4-QAM is used, a generalized optimal diversity (GOD) scheme (3)of Table 1, a quasi-orthogonal code STC scheme (4) of Table 1, A-matrix,proposed in IEEE 802.16e, STC scheme (5) of Table 1, a result ofEquation 17, and a result of Equation 21.

As discussed, the STC performance can changed based on channelenvironment. Further, as illustrated in FIG. 5, the result of Equation17 is an improvement from the conventional optimum STC scheme.

The following is an example of space-time coding that can be applied toa four (4) antennas system.

$\begin{matrix}{C_{{New}\; 1}^{4 \times 2} = \begin{bmatrix}{{w_{1}s_{1}} + {w_{2}s_{2}}} & {{{- w_{1}}s_{1}} + {w_{2}s_{2}}} \\{{w_{3}s_{1}^{*}} - {w_{4}s_{2}^{*}}} & {{w_{3}s_{1}^{*}} + {w_{4}s_{2}^{*}}} \\{{w_{1}s_{3}} + {w_{2}s_{4}}} & {{{- w_{1}}s_{3}} + {w_{2}s_{4}}} \\{{w_{3}s_{3}^{*}} - {w_{4}s_{4}^{*}}} & {{w_{3}s_{3}^{*}} + {w_{4}s_{4}^{*}}}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 24} \right\rbrack\end{matrix}$

In Equation 24, the data symbols are transmitted during two (2) timeslots. That is, space-time coding is performed during two (2) timeslots. Referring to Equation 24, there are a total of four (4) transmitantennas. Here, these four (4) antennas are used to transmit four (4)data symbols, s₁, s₂, s₃, s₄, during two (2) time slots. Further, eachantenna transmits two (2) data symbols during two (2) time slots. Thedata symbols, s₁ and s₂, are transmitted via Antenna #1 and Antenna #2,respectively. Moreover, the weight values, w₁, w₂, w₃, w₄, are appliedto each data symbol, s₁ and s₂. Furthermore, the data symbols, s₃ ands₄, are transmitted via Antenna #3 and Antenna 4, respectively.Similarly, the weight values, w₁, w₂, w₃, w₄, are applied to each datasymbol, s₃ and s₄. As discussed above, the weight values applied to datasymbols can vary/change from one time slot to another, and also from oneantenna to another.

The weights or weight values as shown in Equation 24 can be expressedaccording to Equation 25.

$\begin{matrix}{{w_{1} = \frac{^{j\; \theta_{a}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},\mspace{14mu} {w_{2} = \frac{r\; ^{j\; \theta_{b}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},{w_{3} = \frac{r\; ^{j\; \theta_{c}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},\mspace{14mu} {w_{4} = \frac{^{j\; \theta_{d}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},} & \left\lbrack {{Equation}\mspace{14mu} 25} \right\rbrack\end{matrix}$

Equation 25 is an equation used to describe the weight values used inEquation 24. As such, the weight values can be constructed in differentform and not limited to Equation 24. That is, the weight values ofEquation 25 can be complex number(s) having different values, and notlimited to Equation 25.

The weight values (w₁, w₂, w₃, w₄) can be determined using phase values(θ_(a), θ_(b), θ_(c), θ_(d)) and a real number r. These variable numberscan be of different values. In other words, the variable numbers canhave a different optimal value based on the system, and if thetransmitting/receiving end lacks the channel information, the variablenumber can have optimum capability by satisfying Equation 26.

θ_(a)+θ_(b)=θ_(c)+θ_(d), r=1  [Equation 26]

Preferably, each of the weight values applied in Equation 24 have thesame amplitude, and the sum of the phase of any two (2) weight values issame as the sum of the phase of the remaining two (2) weight values. IfEquation 26 is satisfied, then a minimum product distance (indicated as‘dp.min’ in Table 1) with respect to Equation 24 can be optimized.

The STC scheme of Equation 24 does not provide full diversity. Further,it is preferable that a same modulation level and a same coding level isapplied to the data symbols, which are linearly combined with specificweight values during a specified time slot. For example, the datasymbols, s₁ and s₂, are assigned a first MCS level while the datasymbols, s₃ and s₄ are assigned a second MCS level.

The following is another example of space-time coding that can beapplied to a four (4) antennas system.

$\begin{matrix}{C_{{New}\; 2}^{4 \times 2} = \begin{bmatrix}{{w_{1}{\overset{\sim}{x}}_{1}} + {w_{2}{\overset{\sim}{x}}_{2}}} & {{{- w_{1}}{\overset{\sim}{x}}_{1}} + {w_{2}{\overset{\sim}{x}}_{2}}} \\{{w_{3}{\overset{\sim}{x}}_{1}^{*}} - {w_{4}{\overset{\sim}{x}}_{2}^{*}}} & {{w_{3}{\overset{\sim}{x}}_{1}^{*}} + {w_{4}{\overset{\sim}{x}}_{2}^{*}}} \\{{w_{1}{\overset{\sim}{x}}_{3}} + {w_{2}{\overset{\sim}{x}}_{4}}} & {{{- w_{1}}{\overset{\sim}{x}}_{3}} + {w_{2}{\overset{\sim}{x}}_{4}}} \\{{w_{3}{\overset{\sim}{x}}_{3}^{*}} - {w_{4}{\overset{\sim}{x}}_{4}^{*}}} & {{w_{3}{\overset{\sim}{x}}_{3}^{*}} + {w_{4}{\overset{\sim}{x}}_{4}^{*}}}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 27} \right\rbrack\end{matrix}$

In Equation 27, the data symbols are transmitted during two (2) timeslots. That is, the space-time coding is performed during two (2) timeslots. Referring to Equation 27, x_(i)=s_(i)e^(jθ) ^(r) , where i=1, 2,3, 4, and {tilde over (x)}₁=x₁ ^(R)+jx₃ ^(I), {tilde over (x)}₂=x₂^(R)+jx₄ ^(I), {tilde over (x)}₃=x₃ ^(R)+jx₁ ^(I), and {tilde over(x)}₄=x₄ ^(R)+jx₂ ^(I). Here, the superscript R represents a real numberof a complex number, and J represents an imaginary number of a complexnumber.

Further, all four (4) antennas transmit signals {tilde over (x)}₁,{tilde over (x)}₂, {tilde over (x)}₃, {tilde over (x)}₄ which correspondto data symbols s₁, s₂, s₃, s₄ during four (4) time slots. In addition,since the signals {tilde over (x)}₁, {tilde over (x)}₂, {tilde over(x)}₃, {tilde over (x)}₄ are derived from each of the data symbols s₁,s₂, s₃, s₄, each transmit antenna transmits signals which correspond todata symbols s₁, s₂, s₃, s₄ during the four (4) time slots. Morespecifically, {tilde over (x)}₁ and {tilde over (x)}₂ corresponding tothe data symbols s₁, s₂, s₃, s₄ are transmitted via Antenna #1 andAntenna #2, respectively, the signals are transmitted during the firsttwo time slots out of four (4) time slots, and specific weight valuesw₁, w₂, w₃, w₄ are applied. Furthermore, {tilde over (x)}₃ and {tildeover (x)}₄ corresponding to the data symbols s₁, s₂, s₃, s₄ aretransmitted via Antenna #3 and Antenna #4, respectively, the signals aretransmitted during the last two time slots out of four (4) time slots,and specific weight values w₁, w₂, w₃, w₄ are applied.

In other words, Antenna #1 and Antenna #2 can be used to transmit {tildeover (x)}₁ and {tilde over (x)}₂ corresponding to the data symbols s₁,s₂, s₃, s₄, respectively, and Antenna #3 and Antenna #4 can be used totransmit {tilde over (x)}₁ and {tilde over (x)}₂ corresponding to thedata symbols s₁, s₂, s₃, s₄, respectively. The weight values applied tothe signals, {tilde over (x)}₁, {tilde over (x)}₂, {tilde over (x)}₃,{tilde over (x)}₄, or the weight values applied to the data symbols, s₁,s₂, s₃, s₄, can vary from one time slot to another and can also varyfrom one transmit antenna to another.

The weights or weight values can be expressed as shown in Equation 28.

$\begin{matrix}{{w_{1} = \frac{^{j\; \theta_{a}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},{w_{2} = \frac{r\; ^{j\; \theta_{b}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},{w_{3} = \frac{r\; ^{j\; \theta_{c}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},{w_{4} = \frac{\; ^{j\; \theta_{d}}}{\sqrt{2\left( {1 + r^{2}} \right)}}}} & \left\lbrack {{Equation}\mspace{14mu} 28} \right\rbrack\end{matrix}$

Equation 28 is an equation used to describe the weight values used inEquation 27. As such, the weight values can be constructed in differentform and not limited to Equation 28. That is, the weight values ofEquation 27 can be complex number(s) having different values, and notlimited to Equation 28.

The weight values (w₁, w₂, w₃, w₄) can be determined using phase values,θ_(a), θ_(b), θ_(c), θ_(d) and a real number r. These variable numberscan be of different values. In other words, the variable numbers canhave a different optimal value based on the system, and if thetransmitting/receiving end lacks the channel information, the variablenumber can have optimum capability by satisfying Equation 29 andEquation 30.

θ_(a)+θ_(b)=θ_(c)+θ_(d), r=1  [Equation 29]

Preferably, each of the weight values applied in Equation 28 have thesame amplitude, and the sum of the phase of any two (2) weight values issame as the sum of the phase of the remaining two (2) weight values.

$\begin{matrix}{\theta_{r} = {\frac{1}{2}{\tan^{- 1}(2)}}} & \left\lbrack {{Equation}\mspace{14mu} 30} \right\rbrack\end{matrix}$

θ_(r) can be used to determine x_(i) and s_(i).

The STC of Equation 27 does not provide full diversity. However, {tildeover (x)}₁ and {tilde over (x)}₂ corresponding to the data symbols s₁,s₂, s₃, s₄ are transmitted via Antenna #1 and Antenna #2, respectively,the signals are transmitted. Furthermore, {tilde over (x)}₁ and {tildeover (x)}₄ corresponding to the data symbols s₁, s₂, s₃, s₄ aretransmitted via Antenna #3 and Antenna #4, respectively. Further, all ofthe data symbols, s₁, s₂, s₃, s₄, are combined during a specified timeslot and then transmitted. Preferably, a same MCS level is assigned toall of the data symbols.

The following is another example of space-time coding that can be usedin a four (4) antenna system in which the spatial multiplexing rate is2. The following is based on Equation 11.

$\begin{matrix}{C_{{New}\; 3}^{4\; x\; 2} = \begin{bmatrix}{{w_{1}{\overset{\sim}{x}}_{1}} + {w_{2}{\overset{\sim}{x}}_{2}} + {w_{3}{\overset{\sim}{x}}_{3}} + {w_{4}{\overset{\sim}{x}}_{4}}} & {{{- w_{1}}{\overset{\sim}{x}}_{1}} - {w_{2}{\overset{\sim}{x}}_{2}} + {w_{3}{\overset{\sim}{x}}_{3}} + {w_{4}{\overset{\sim}{x}}_{4}}} & 0 & 0 \\{{w_{5}{\overset{\sim}{x}}_{1}} + {w_{6}{\overset{\sim}{x}}_{2}} - {w_{7}{\overset{\sim}{x}}_{3}} - {w_{8}{\overset{\sim}{x}}_{4}}} & {{w_{5}{\overset{\sim}{x}}_{1}} + {w_{6}{\overset{\sim}{x}}_{2}} + {w_{7}{\overset{\sim}{x}}_{3}} + {w_{8}{\overset{\sim}{x}}_{4}}} & 0 & 0 \\0 & 0 & {{w_{1}{\overset{\sim}{x}}_{5}} + {w_{2}{\overset{\sim}{x}}_{6}} + {w_{3}{\overset{\sim}{x}}_{7}} + {w_{4}{\overset{\sim}{x}}_{8}}} & {{{- w_{1}}{\overset{\sim}{x}}_{5}} - {w_{2}{\overset{\sim}{x}}_{6}} + {w_{3}{\overset{\sim}{x}}_{7}} + {w_{4}{\overset{\sim}{x}}_{8}}} \\0 & 0 & {{w_{5}{\overset{\sim}{x}}_{5}} + {w_{6}{\overset{\sim}{x}}_{6}} - {w_{7}{\overset{\sim}{x}}_{7}} - {w_{8}{\overset{\sim}{x}}_{8}}} & {{w_{5}{\overset{\sim}{x}}_{5}} + {w_{6}{\overset{\sim}{x}}_{6}} + {w_{7}{\overset{\sim}{x}}_{7}} + {w_{8}{\overset{\sim}{x}}_{8}}}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 31} \right\rbrack\end{matrix}$

Referring to Equation 31, x_(i)=s_(i)e^(jθ) ^(r) , where i=1, 2, . . . ,8, and {tilde over (x)}₁=x₁ ^(R)+jx₅ ^(I), {tilde over (x)}₂=x₂ ^(R)+jx₆^(I), {tilde over (x)}₃=x₃ ^(R)+jx₇ ^(I), {tilde over (x)}₄=x₄ ^(R)+jx₈^(I), {tilde over (x)}₅=x₅ ^(R)+jx₁ ^(I), {tilde over (x)}₆=x₆ ^(R)+jx₂^(I), {tilde over (x)}₇=x₇ ^(R)+jx₃ ^(I), and {tilde over (x)}₈=x₈^(R)+jx₄ ^(I). Here, the superscript R represents a real number of acomplex number, and I represents an imaginary number of a complexnumber.

In Equation 31, a total of four (4) antennas transmit signals {tildeover (x)}₁, {tilde over (x)}₂, {tilde over (x)}₃, {tilde over (x)}₄,{tilde over (x)}₅, {tilde over (x)}₆, {tilde over (x)}₇, {tilde over(x)}₈ which correspond to data symbols s₁, s₂, s₃, s₄, s₅, s₆, s₇, s₈during four (4) time slots. Furthermore, since the signals {tilde over(x)}₁, {tilde over (x)}₂, {tilde over (x)}₃, {tilde over (x)}₄, {tildeover (x)}₅, {tilde over (x)}₆, {tilde over (x)}₇, {tilde over (x)}₈ arederived from each of the data symbols, s₁, s₂, s₃, s₄, s₅, s₆, s₇, s₈,each transmit antenna transmits signals which correspond to data symbolss₁, s₂, s₃, s₄, s₅, s₆, s₇, s₈ during the four (4) time slots.

More specifically, {tilde over (x)}₁, {tilde over (x)}₂, {tilde over(x)}₃, {tilde over (x)}₄ corresponding to the data symbols s₁, s₂, s₃,s₄, s₅, s₆, s₇, s₈ are transmitted via Antenna #1 and Antenna #2,respectively, the signals are transmitted during the first two timeslots out of four (4) time slots, and specific weight values w₁, w₂, w₃,w₄, w₅, w₆, w₇, w₈ are applied. Additionally, {tilde over (x)}₅, {tildeover (x)}₆, {tilde over (x)}₇, {tilde over (x)}₈ corresponding to thedata symbols s₁, s₂, s₃, s₄, s₅, s₆, s₇, s₈ are transmitted via Antenna#3 and Antenna #4, respectively, the signals are transmitted during thelast two time slots out of four (4) time slots, and specific weightvalues w₁, w₂, w₃, w₄, w₅, w₆, w₇, w₈ are applied.

In other words, Antenna #1 and Antenna #2 can be used to transmit {tildeover (x)}₁, {tilde over (x)}₂, {tilde over (x)}₃, {tilde over (x)}₄corresponding to the data symbols s₁, s₂, s₃, s₄, s₅, s₆, s₇, s₈,respectively, and Antenna #3 and Antenna #4 can be used to transmit{tilde over (x)}₅, {tilde over (x)}₆, {tilde over (x)}₇, {tilde over(x)}₈ corresponding to the data symbols s₁, s₂, s₃, s₄, s₅, s₆, s₇, s₈,respectively. The weight values applied to the signals, {tilde over(x)}₁, {tilde over (x)}₂, {tilde over (x)}₃, {tilde over (x)}₄, or theweight values applied to the data symbols, s₁, s₂, s₃, s₄, can vary fromone time slot to another and can also vary from one transmit antenna toanother.

Equation 32 shows the weight values related to Equation 21.

$\begin{matrix}{{{w_{1} = \frac{^{j\; \theta_{a}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{2} = \frac{r\; ^{j\; \theta_{b}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{3} = \frac{^{j\; \theta_{c}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{4} = \frac{r\; ^{j\; \theta_{d}}}{\sqrt{4\left( {1 + r^{2}} \right)}}}}{{w_{5} = \frac{r\; ^{j\; \theta_{e}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{6} = \frac{^{j\; \theta_{f}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{7} = \frac{r\; ^{j\; \theta_{g}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{8} = \frac{^{j\; \theta_{h}}}{\sqrt{4\left( {1 + r^{2}} \right)}}}}} & \left\lbrack {{Equation}\mspace{14mu} 32} \right\rbrack\end{matrix}$

Here, Equation 32 is an equation used to describe the weight values usedin Equation 31. As such, the weight values can be constructed indifferent form and not limited to Equation 32. That is, the weightvalues of Equation 31 can be complex number(s) having different values,and not limited to Equation 32.

Referring to the weight values of Equation 32, w₁, w₃, w₄, w₇, w₈ aredetermined by phase values, θ_(a), θ_(b), θ_(c), θ_(d), θ_(e), θ_(h),and a real number, r. As such, these variable numbers can be ofdifferent values. In other words, the variable numbers can have adifferent optimal value based on the system, and if thetransmitting/receiving end lacks the channel information, the variablenumber can have optimum capability by satisfying Equation 33.

$\begin{matrix}{{r = \frac{\sqrt{5} \pm 1}{2}},{\theta_{a} = {\theta_{b} = {\theta_{c} = {\theta_{d} = 0}}}},{\theta_{e} = \frac{3\; \pi}{2}},{\theta_{f} = \frac{\pi}{2}},{\theta_{g} = \pi},{\theta_{h} = 0}} & \left\lbrack {{Equation}\mspace{14mu} 33} \right\rbrack\end{matrix}$

That is, referring to Equation 33, preferably, w₁, w₂, w₃, w₄, w₇, w₈are real numbers, w₅, w₆ are imaginary numbers, and r times thespecified amplitude exists between w₁, w₃, w₆, w₈ and w₂, w₄, w₅, w₇.Here, r can be

$\frac{\sqrt{5} + 1}{2}{\mspace{11mu} \;}{or}\mspace{14mu} {\frac{\sqrt{5} - 1}{2}.}$

$\begin{matrix}{\theta_{r} = \frac{\pi}{36}} & \left\lbrack {{Equation}\mspace{14mu} 34} \right\rbrack\end{matrix}$

θ_(r) can be used to determine x_(i) and s_(i), preferably.

If the STC schemes discussed with respect to Equations 24, 27, and 31are used, a same performance result can be obtained to that of the STCscheme (6) of Table 1. Space-time coding can be of different types basedon the weight values, and an improved result can be obtained compared tothe conventional coding depending on the channel condition.

The STC of Equation 27 does not provide full diversity. However, {tildeover (x)}₁, {tilde over (x)}₂, {tilde over (x)}₃, {tilde over (x)}₄corresponding to the data symbols s₁, s₂, s₃, s₄, s₅, s₆, s₇, s₈ aretransmitted via Antenna #1 and Antenna #2, respectively, the signals aretransmitted. Furthermore, {tilde over (x)}₅, {tilde over (x)}₆, {tildeover (x)}₇, {tilde over (x)}₈ corresponding to the data symbols s₁, s₂,s₃, s₄, s₅, s₆, s₇, s₈ are transmitted via Antenna #3 and Antenna #4,respectively. Further, all of the data symbols, s₁, s₂, s₃, s₄, s₅, s₆,s₇, s₈, are combined during a specified time slot and then transmitted.Preferably, a same MCS level is uniformly assigned to all of the datasymbols.

As discussed, the STC scheme according to the embodiment of the presentinvention can be further explained with space-time coded matrix C. Thatis, space-time coding can be performed using the STC schemes ofEquations 7, 11, 14, 17, 21, 24, 27, and 31. The aforementionedequations are examples of the STC schemes, and the STC matrix of theseequations can be modified into a new or different STC matrix by aunitary matrix. That is, a unitary matrix can be multiplied to the STCmatrix to form a different or a new STC matrix.

A unitary matrix, U, can be shown according to Equation 35.

U×U ^(H) =I, det(U)=1  [Equation 35]

If the STC matrix discussed in the embodiments of the present inventionis referred to as C, the U matrix multiplied STC matrix can be expressedas follows.

det(C×U)=det(C)det(U)=det(C)  [Equation 36]

In other words, if the unitary matrix is multiplied to the STC matrix,the determinant of the original STC matrix is unaffected or unchanged.As such, the performance of the original STC matrix is unchanged.

An example of modified STC matrix by multiplying the unitary matrix canbe shown in Equation 37. Here, the unitary matrix is multiplied to theSTC matrix of Equation 10.

$\begin{matrix}{{C_{New}^{2\; x\; 1} = {\frac{1}{\sqrt{4}}\begin{bmatrix}{s_{1} + s_{2}} & {{- s_{1}} + s_{2}} \\{s_{1}^{*} - s_{2}^{*}} & {s_{1}^{*} + s_{2}^{*}}\end{bmatrix}}},{U = \begin{pmatrix}0 & 1 \\1 & 0\end{pmatrix}},{{C_{New}^{2\; x\; 1}x\; U} = {\frac{1}{\sqrt{4}}\begin{bmatrix}{{- s_{1}} + s_{2}} & {s_{1} + s_{2}} \\{s_{1}^{*} + s_{2}^{*}} & {s_{1}^{*} - s_{2}^{*}}\end{bmatrix}}}} & \left\lbrack {{Equation}\mspace{14mu} 37} \right\rbrack\end{matrix}$

With respect to Equation 37, the determinants for C_(New) ^(2×1),C_(New) ^(2×1)×U are as follows.

$\begin{matrix}\begin{matrix}{{\det \left( C_{New}^{2\; x\; 1} \right)} = {\det \left( {\frac{1}{\sqrt{4}}\begin{pmatrix}{s_{1} + s_{2}} & {{- s_{1}} + s_{2}} \\{s_{1}^{*} - s_{2}^{*}} & {s_{1}^{*} + s_{2}^{*}}\end{pmatrix}} \right)}} \\{= {{s_{1}}^{2} + {s_{2}}^{2}}} \\{{\det \left( {C_{New}^{2\; x\; 1}x\; U} \right)} = {\det \left( {\frac{1}{2}\begin{pmatrix}{s_{1} + s_{2}} & {{- s_{1}} + s_{2}} \\{s_{1}^{*} - s_{2}^{*}} & {s_{1}^{*} + s_{2}^{*}}\end{pmatrix}\begin{pmatrix}0 & 1 \\1 & 0\end{pmatrix}} \right)}} \\{= {\det \left( {\frac{1}{2}\begin{pmatrix}{{- s_{1}} + s_{2}} & {s_{1} + s_{2}} \\{s_{1}^{*} + s_{2}^{*}} & {s_{1}^{*} - s_{2}^{*}}\end{pmatrix}} \right)}} \\{= {{s_{1}}^{2} + {s_{2}}^{2}}}\end{matrix} & \left\lbrack {{Equation}\mspace{14mu} 38} \right\rbrack\end{matrix}$

As discussed, a unitary matrix can be multiplied to a specified STCmatrix to make a modified matrix as shown as an example in Equation 38.

With respect to the embodiments of the present invention, the weightvalues (also referred to as complex weights) of the space-time codes canbe applied to an orthogonal frequency division multiplexing (OFDM)system. If the weight values of the STC are applied to the OFDM system,then different weight values can be applied based on frequency carrierindex. FIG. 6 illustrates subcarriers in an OFDM frequency domain. Here,the system can be represented by N−1 number of subcarriers.

It will be apparent to those skilled in the art that variousmodifications and variations can be made in the present inventionwithout departing from the spirit or scope of the inventions. Thus, itis intended that the present invention covers the modifications andvariations of this invention provided they come within the scope of theappended claims and their equivalents.

1. A method of transmitting space-time coded data in a wirelesscommunication system having a plurality of antennas, the methodcomprising: allocating data symbols combined with complex weights to atleast two transmit antennas during at least one specified time slot; andtransmitting the data symbols combined with complex weights to areceiving end via the at least two transmit antennas during the at leastone specified time slot.
 2. The method of claim 1, wherein a sum of asecond power of an absolute value of the complex weights is same foreach transmit antenna during the same time slot.
 3. The method of claim1, wherein a total power of the transmit antennas during the same timeslot is the same.
 4. The method of claim 1, wherein the complex weightsvary from one time slot to another time slot.
 6. The method of claim 1,wherein the complex weight has a value other than
 0. 7. The method ofclaim 1, wherein the complex weights which are combined with the datasymbols are the same when retransmitted.
 8. The method of claim 1,wherein the complex weights which are combined with the data symbols aredifferent when retransmitted.
 9. The method of claim 1, wherein eachcomplex weight is allocated according to a subcarrier index in anOrthogonal Frequency Division Multiplexing (OFDM)-based system.
 10. Themethod of claim 1, wherein the complex weight is determined by thetransmit antenna which is assigned for transmitting the data symbols.11. The method of claim 1, wherein each of the complex weights has sameamplitude.
 12. The method of claim 1, wherein a number of the datasymbols to be transmitted is determined by any one of available transmitantennas or a spatial multiplexing rate.
 13. The method of claim 1,wherein all of the data symbols are applied a same modulation scheme.14. The method of claim 1, wherein all of the data symbols are applied asame coding scheme.
 15. A method of transmitting space-time coded datain a wireless communication system having a plurality of antennas, themethod comprising: allocating data symbols to at least two transmitantennas during at least one specified time slot; and transmitting thedata symbols to a receiving end via the at least two transmit antennasduring the at least one specified time slot, wherein the data symbolsare combined with complex weights.
 16. The method of claim 15, whereinthe data symbols are allocated to two transmit antennas during two timeslots according to a space-time code matrix, C, which is expressed as$C = {\begin{bmatrix}{{w_{1}s_{1}} + {w_{2}s_{2}}} & {{{- w_{1}}s_{1}} + {w_{2}s_{2}}} \\{{w_{3}s_{1}^{*}} - {w_{4}s_{2}^{*}}} & {{w_{3}s_{1}^{*}} + {w_{4}s_{2}^{*}}}\end{bmatrix}.}$
 17. The method of claim 16, wherein the complexweights, w₁, w₂, w₃, w₄, have the same amplitude, and a sum of phases,w₁ and w₃, and a sum of phases, w₂ and w₄, are the same.
 18. The methodof claim 16, wherein the complex weights, w₁, w₂, w₃, w₄, have differentamplitudes, and a sum of phases, w₁ and w₃, and a sum of phases, w₂ andw₄, are the same.
 19. The method of claim 16, wherein the complexweights, w₁, w₂, w₃, w₄, are defined as${w_{1} = \frac{^{j\; \theta_{a}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},{w_{2} = \frac{r\; ^{j\; \theta_{b}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},{w_{3} = \frac{r\; ^{j\; \theta_{c}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},{w_{4} = \frac{\; ^{j\; \theta_{d}}}{\sqrt{2\left( {1 + r^{2}} \right)}}}$in which r represents a real number and values of the phases are denotedas θ_(a), θ_(b), θ_(c), θ_(d).
 20. The method of claim 15, wherein thedata symbols are allocated to two transmit antennas during two timeslots according to a space-time code matrix, C, which is expressed as$C = {\begin{bmatrix}{{w_{1}s_{1}} + {w_{2}s_{2}} + {w_{3}s_{3}} + {w_{4}s_{4}}} & {{{- w_{1}}s_{1}} - {w_{2}s_{2}} + {w_{3}s_{3}} + {w_{4}s_{4}}} \\{{w_{5}s_{1}} + {w_{6}s_{2}} - {w_{7}s_{3}} - {w_{8}s_{4}}} & {{w_{5}s_{1}} + {w_{6}s_{2}} + {w_{7}s_{3}} + {w_{8}s_{4}}}\end{bmatrix}.}$
 21. The method of claim 20, wherein the complexweights, w₂, w₄, w₅, w₇, have the same amplitude, the complex weights,w₁, w₃, w₆, w₈, have the same amplitude, and the amplitude of thecomplex weights, w₂, w₄, w₅, w₇, is r times the size of the complexweights, w₁, w₃, w₆, w₈.
 22. The method of claim 20, wherein the complexnumbers, w₁, w₂, w₃, w₄, w₇, w₈, are pure real numbers and the complexnumbers, w₅, w₆, are pure imaginary numbers.
 23. The method of claim 20,wherein the complex weights, w₁, w₂, w₃, w₄, w₅, w₆, w₇, w₈, are definedas${w_{1} = \frac{^{j\; \theta_{a}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{2} = \frac{r\; ^{j\; \theta_{b}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{3} = \frac{^{j\; \theta_{c}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{4} = \frac{r\; ^{j\; \theta_{d}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{5} = \frac{r\; ^{j\; \theta_{e}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{6} = \frac{^{j\; \theta_{f}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{7} = \frac{r\; ^{j\; \theta_{g}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{8} = \frac{^{j\; \theta_{h}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},$in which r represents a real number and values of the phases are denotedas θ_(a), θ_(b), θ_(c), θ_(d), θ_(e), θ_(f), θ_(g), θ_(h).
 24. Themethod of claim 23, wherein the real number, r, and the phases, θ_(a),θ_(b), θ_(c), θ_(d), θ_(e), θ_(f), θ_(g), θ_(h), are defined as${r = \frac{\sqrt{5} \pm 1}{2}},{\theta_{a} = {\theta_{b} = {\theta_{c} = {\theta_{d} = 0}}}},{\theta_{e} = \frac{3\; \pi}{2}},{\theta_{f} = \frac{\pi}{2}},{\theta_{g} = \pi},{\theta_{h} = 0.}$25. The method of claim 15, wherein the data symbols are allocatedaccording to a space-time code matrix, C, and the space-time codematrix, C, is multiplied to a unitary matrix.
 26. The method of claim15, wherein the data symbols are allocated to four transmit antennasduring four time slots according to a space-time code matrix, C, whichis expressed as $C = {\begin{bmatrix}{{w_{1}s_{1}} + {w_{2}s_{2}}} & {{{- w_{1}}s_{1}} + {w_{2}s_{2}}} & 0 & 0 \\{{w_{3}s_{1}^{*}} - {w_{4}s_{2}^{*}}} & {{w_{3}s_{1}^{*}} + {w_{4}s_{2}^{*}}} & 0 & 0 \\0 & 0 & {{w_{1}s_{3}} + {w_{2}s_{4}}} & {{{- w_{1}}s_{3}} + {w_{2}s_{4}}} \\0 & 0 & {{w_{3}s_{3}^{*}} - {w_{4}s_{4}^{*}}} & {{w_{3}s_{3}^{*}} + {w_{4}s_{4}^{*}}}\end{bmatrix}.}$
 27. The method of claim 26, wherein the complexweights, w₁, w₂, w₃, w₄, have the same amplitude, and a sum of phases,w₁ and w₃, and a sum of phases, w₂ and w₄, are the same.
 28. The methodof claim 26, wherein the complex weights, w₁, w₂, w₃, w₄, have differentamplitudes, and a sum of phases, w₁ and w₃, and a sum of phases, w₂ andw₄, are the same.
 29. The method of claim 26, wherein the complexweights, w₁, w₂, w₄, are defined as${w_{1} = \frac{^{j\; \theta_{a}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},{w_{2} = \frac{r\; ^{j\; \theta_{b}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},{w_{3} = \frac{r\; ^{j\; \theta_{c}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},{w_{4} = \frac{^{j\; \theta_{d}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},$in which r represents a real number and values of the phases are denotedas θ_(a), θ_(b), θ_(c), θ_(d).
 30. The method of claim 15, wherein thedata symbols are allocated to four transmit antennas during four timeslots according to a space-time code matrix, C, which is expressed as$C = {\begin{bmatrix}{{w_{1}{\overset{\sim}{x}}_{1}} + {w_{2}{\overset{\sim}{x}}_{2}}} & {{{- w_{1}}{\overset{\sim}{x}}_{1}} + {w_{2}{\overset{\sim}{x}}_{2}}} & 0 & 0 \\{{w_{3}{\overset{\sim}{x}}_{1}^{*}} - {w_{4}{\overset{\sim}{x}}_{2}^{*}}} & {{w_{3}{\overset{\sim}{x}}_{1}^{*}} + {w_{4}{\overset{\sim}{x}}_{2}^{*}}} & 0 & 0 \\0 & 0 & {{w_{1}{\overset{\sim}{x}}_{3}} + {w_{2}{\overset{\sim}{x}}_{4}}} & {{{- w_{1}}{\overset{\sim}{x}}_{3}} + {w_{2}{\overset{\sim}{x}}_{4}}} \\0 & 0 & {{w_{3}{\overset{\sim}{x}}_{3}^{*}} - {w_{4}{\overset{\sim}{x}}_{4}^{*}}} & {{w_{3}{\overset{\sim}{x}}_{3}^{*}} + {w_{4}{\overset{\sim}{x}}_{4}^{*}}}\end{bmatrix}.}$
 31. The method of claim 30, wherein the symbols, {tildeover (x)}₁, {tilde over (x)}₂, {tilde over (x)}₃, {tilde over (x)}₄, aredefined as {tilde over (x)}=x₁ ^(R)+jx₃ ^(I), {tilde over (x)}₂=x₂^(R)+jx₄ ^(I), {tilde over (x)}₃=x₃ ^(R)+jx₁ ^(I), and {tilde over(x)}₄=x₄ ^(R)+jx₂ ^(I) and wherein x_(i)=s_(i)e^(jθ) ^(r) .
 32. Themethod of claim 30, wherein the complex weights, w₁, w₂, w₃, w₄, havethe same amplitude, and a sum of phases, w₁ and w₃, and a sum of phases,w₂ and w₄, are the same.
 33. The method of claim 30, wherein the complexweights, w₁, w₂, w₃, w₄, have different amplitudes, and a sum of phases,w₂ and w₃, and a sum of phases, w₂ and w₄, are the same.
 34. The methodof claim 32, wherein value of the phase is θ_(r), which is defined as$\theta_{r} = {\frac{1}{2}{{\tan^{- 1}(2)}.}}$
 35. The method of claim30, wherein the complex weights, w₁, w₂, w₃, w₄, are defined as${w_{1} = \frac{^{j\; \theta_{a}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},{w_{2} = \frac{r\; ^{j\; \theta_{b}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},{w_{3} = \frac{r\; ^{j\; \theta_{c}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},{w_{4} = \frac{^{j\; \theta_{d}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},$in which r represents a real number and values of the phases are denotedas θ_(a), θ_(b), θ_(c), θ_(d).
 36. The method of claim 15, wherein thedata symbols are allocated to four transmit antennas during four timeslots according to a space-time code matrix, C, which is expressed as$C = \begin{bmatrix}\begin{matrix}{{w_{1}s_{1}} + {w_{2}s_{2}} +} \\{{w_{3}s_{3}} + {w_{4}s_{4}}}\end{matrix} & \begin{matrix}{{{- w_{1}}s_{1}} - {w_{2}s_{2}} +} \\{{w_{3}s_{3}} + {w_{4}s_{4}}}\end{matrix} & 0 & 0 \\\begin{matrix}{{w_{5}s_{1}} + {w_{6}s_{2}} -} \\{{w_{7}s_{3}} - {w_{8}s_{4}}}\end{matrix} & \begin{matrix}{{w_{5}s_{1}} + {w_{6}s_{2}} +} \\{{w_{7}s_{3}} + {w_{8}s_{4}}}\end{matrix} & 0 & 0 \\0 & 0 & \begin{matrix}{{w_{1}s_{1}} + {w_{2}s_{2}} +} \\{{w_{3}s_{3}} + {w_{4}s_{4}}}\end{matrix} & \begin{matrix}{{{- w_{1}}s_{1}} - {w_{2}s_{2}} +} \\{{w_{3}s_{3}} + {w_{4}s_{4}}}\end{matrix} \\0 & 0 & \begin{matrix}{{w_{5}s_{1}} + {w_{6}s_{2}} -} \\{{w_{7}s_{3}} - {w_{8}s_{4}}}\end{matrix} & \begin{matrix}{{w_{5}s_{1}} + {w_{6}s_{2}} +} \\{{w_{7}s_{3}} + {w_{8}s_{4}}}\end{matrix}\end{bmatrix}$
 37. The method of claim 36, wherein the complex weights,w₁, w₂, w₃, w₄, w₅, w₆, w₇, w₈, are defined as${w_{1} = \frac{^{j\; \theta_{a}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{2} = \frac{r\; ^{j\; \theta_{b}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{3} = \frac{^{j\; \theta_{c}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{4} = \frac{r\; ^{j\; \theta_{d}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{5} = \frac{r\; ^{j\; \theta_{e}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{6} = \frac{^{j\; \theta_{f}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{7} = \frac{r\; ^{j\; \theta_{g}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{8} = \frac{^{j\; \theta_{h}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},$in which r represents a real number and values of the phases are denotedas a θ_(a), θ_(b), θ_(c), θ_(d), θ_(f), θ_(g), θ_(h).
 38. The method ofclaim 36, wherein the real number, r, and the phases, θ_(a), θ_(b),θ_(c), θ_(d), θ_(f), θ_(g), θ_(h), are defined as${r = \frac{\sqrt{5} \pm 1}{2}},{\theta_{a} = {\theta_{b} = {\theta_{c} = {\theta_{d} = 0}}}},{\theta_{e} = \frac{3\; \pi}{2}},{\theta_{f} = \frac{\pi}{2}},{\theta_{g} = \pi},{\theta_{h} = 0.}$39. The method of claim 15, wherein the data symbols are allocated tofour transmit antennas during two time slots according to a space-timecode matrix, C, which is expressed as $C = {\begin{bmatrix}{{w_{1}s_{1}} + {w_{2}s_{2}}} & {{{- w_{1}}s_{1}} + {w_{2}s_{2}}} \\{{w_{3}s_{1}^{*}} - {w_{4}s_{2}^{*}}} & {{w_{3}s_{1}^{*}} + {w_{4}s_{2}^{*}}} \\{{w_{1}s_{3}} + {w_{2}s_{4}}} & {{{- w_{1}}s_{3}} + {w_{2}s_{4}}} \\{{w_{3}s_{3}^{*}} - {w_{4}s_{4}^{*}}} & {{w_{3}s_{3}^{*}} + {w_{4}s_{4}^{*}}}\end{bmatrix}.}$
 40. The method of claim 39, wherein the complexweights, w₁, w₂, w₃, w₄, have the same amplitude, and a sum of phases,w₁ and w₃, and a sum of phases, w₂ and w₄, are the same.
 41. The methodof claim 39, wherein the complex weights, w₁, w₂, w₃, w₄, have differentamplitudes, and a sum of phases, w₁ and w₃, and a sum of phases, w₂ andw₄, are the same.
 42. The method of claim 39, wherein the complexweights, w₁, w₂, w₃, w₄, are defined as${w_{1} = \frac{^{j\; \theta_{a}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},{w_{2} = \frac{r\; ^{j\; \theta_{b}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},{w_{3} = \frac{r\; ^{j\; \theta_{c}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},{w_{4} = \frac{^{j\; \theta_{d}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},$in which r represents a real number and values of the phases are denotedas θ_(a), θ_(b), θ_(c), θ_(d).
 43. The method of claim 15, wherein thedata symbols are allocated to four transmit antennas during two timeslots according to a space-time code matrix, C, which is expressed as$C = {\begin{bmatrix}{{w_{1}{\overset{\sim}{x}}_{1}} + {w_{2}{\overset{\sim}{x}}_{2}}} & {{{- w_{1}}{\overset{\sim}{x}}_{1}} + {w_{2}{\overset{\sim}{x}}_{2}}} \\{{w_{3}{\overset{\sim}{x}}_{1}^{*}} - {w_{4}{\overset{\sim}{x}}_{2}^{*}}} & {{w_{3}{\overset{\sim}{x}}_{1}^{*}} + {w_{4}{\overset{\sim}{x}}_{2}^{*}}} \\{{w_{1}{\overset{\sim}{x}}_{3}} + {w_{2}{\overset{\sim}{x}}_{4}}} & {{{- w_{1}}{\overset{\sim}{x}}_{3}} + {w_{2}{\overset{\sim}{x}}_{4}}} \\{{w_{3}{\overset{\sim}{x}}_{3}^{*}} - {w_{4}{\overset{\sim}{x}}_{4}^{*}}} & {{w_{3}{\overset{\sim}{x}}_{3}^{*}} + {w_{4}{\overset{\sim}{x}}_{4}^{*}}}\end{bmatrix}.}$
 44. The method of claim 43, wherein the symbols, {tildeover (x)}₁, {tilde over (x)}₂, {tilde over (x)}₃, {tilde over (x)}₄, aredefined as and {tilde over (x)}₁=x₁ ^(R)+jx₃ ^(I), {tilde over (x)}₂=x₂^(R)+jx₄ ^(I), {tilde over (x)}₃=x₃ ^(R)+jx₁ ^(I), and {tilde over(x)}₄=x₄ ^(R)+jx₂ ^(I), and wherein x_(i)=s_(i)e^(jθ) ^(r) .
 45. Themethod of claim 43, wherein the complex weights, w₁, w₂, w₃, w₄, havethe same amplitude, and a sum of phases, w₁ and w₃, and a sum of phases,w₂ and w₄, are the same.
 46. The method of claim 45, wherein value ofthe phase is θ_(r), which is defined as$\theta_{r} = {\frac{1}{2}{{\tan^{- 1}(2)}.}}$
 47. The method of claim43, wherein the complex weights, w₁, w₂, w₃, w₄, are defined as${w_{1} = \frac{^{j\; \theta_{a}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},{w_{2} = \frac{r\; ^{j\; \theta_{b}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},{w_{3} = \frac{r\; ^{j\; \theta_{c}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},{w_{4} = \frac{^{j\; \theta_{d}}}{\sqrt{2\left( {1 + r^{2}} \right)}}},$in which r represents a real number and values of the phases are denotedas θ_(a), θ_(b), θ_(c), θ_(d).
 48. The method of claim 15, wherein thedata symbols are allocated to four transmit antennas during four timeslots according to a space-time code matrix, C, which is expressed as$C_{{New}\; 3}^{4 \times 2} = {\quad\left\lbrack \begin{matrix}\begin{matrix}{{w_{1}{\overset{\sim}{x}}_{1}} + {w_{2}{\overset{\sim}{x}}_{2}} +} \\{{w_{3}{\overset{\sim}{x}}_{3}} + {w_{4}{\overset{\sim}{x}}_{4}}}\end{matrix} & \begin{matrix}{{{- w_{1}}{\overset{\sim}{x}}_{1}} - {w_{2}{\overset{\sim}{x}}_{2}} +} \\{{w_{3}{\overset{\sim}{x}}_{3}} + {w_{4}{\overset{\sim}{x}}_{4}}}\end{matrix} & 0 & 0 \\\begin{matrix}{{w_{5}{\overset{\sim}{x}}_{1}} + {w_{6}{\overset{\sim}{x}}_{2}} -} \\{{w_{7}{\overset{\sim}{x}}_{3}} - {w_{8}{\overset{\sim}{x}}_{4}}}\end{matrix} & \begin{matrix}{{w_{5}{\overset{\sim}{x}}_{1}} + {w_{6}{\overset{\sim}{x}}_{2}} +} \\{{w_{7}{\overset{\sim}{x}}_{3}} + {w_{8}{\overset{\sim}{x}}_{4}}}\end{matrix} & 0 & 0 \\0 & 0 & \begin{matrix}{{w_{1}{\overset{\sim}{x}}_{5}} + {w_{2}{\overset{\sim}{x}}_{6}} +} \\{{w_{3}{\overset{\sim}{x}}_{7}} + {w_{4}{\overset{\sim}{x}}_{8}}}\end{matrix} & \begin{matrix}{{{- w_{1}}{\overset{\sim}{x}}_{5}} - {w_{2}{\overset{\sim}{x}}_{6}} +} \\{{w_{3}{\overset{\sim}{x}}_{7}} + {w_{4}{\overset{\sim}{x}}_{8}}}\end{matrix} \\0 & 0 & \begin{matrix}{{w_{5}{\overset{\sim}{x}}_{5}} + {w_{6}{\overset{\sim}{x}}_{6}} -} \\{{w_{7}{\overset{\sim}{x}}_{7}} - {w_{8}{\overset{\sim}{x}}_{8}}}\end{matrix} & \begin{matrix}{{w_{5}{\overset{\sim}{x}}_{5}} + {w_{6}{\overset{\sim}{x}}_{6}} +} \\{{w_{7}{\overset{\sim}{x}}_{7}} + {w_{8}{\overset{\sim}{x}}_{8}}}\end{matrix}\end{matrix} \right\rbrack}$
 49. The method of claim 48, wherein thesymbols, {tilde over (x)}₁, {tilde over (x)}₂, {tilde over (x)}₃, {tildeover (x)}₄, {tilde over (x)}₅, {tilde over (x)}₆, {tilde over (x)}₇,{tilde over (x)}₁, are defined as {tilde over (x)}₁=x₁ ^(R)+jx₅ ^(I),{tilde over (x)}₁=x₂ ^(R)+jx₆ ^(I), {tilde over (x)}₃=x₃ ^(R)+jx₇ ^(I),{tilde over (x)}₁=x₄ ^(I)+jx₈ ^(I), {tilde over (x)}₅=x₅ ^(R)+jx₁ ^(I),{tilde over (x)}₆=x₆ ^(R)+jx₂ ^(I), {tilde over (x)}₇=x₇ ^(R)+jx₃ ^(I),and {tilde over (x)}₈=x₈ ^(R)+jx₄ ^(I), and wherein x_(i)=s_(i)e^(jθ)^(r) .
 50. The method of claim 48, wherein the complex weights, w₁, w₂,w₃, w₄, w₅, w₆, w₇, w₈, are defined as${w_{1} = \frac{^{j\; \theta_{a}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{2} = \frac{r\; ^{j\; \theta_{b}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{3} = \frac{^{j\; \theta_{c}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{4} = \frac{r\; ^{j\; \theta_{d}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{5} = \frac{r\; ^{j\; \theta_{e}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{6} = \frac{^{j\; \theta_{f}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{7} = \frac{r\; ^{j\; \theta_{g}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},{w_{8} = \frac{^{j\; \theta_{h}}}{\sqrt{4\left( {1 + r^{2}} \right)}}},$in which r represents a real number and values of the phases are denotedas θ_(a), θ_(b), θ_(c), θ_(d), θ_(e), θ_(f), θ_(g), θ_(h).
 51. Themethod of claim 50, wherein the real number, r, and the phases, θ_(a),θ_(b), θ_(c), θ_(d), θ_(e), θ_(f), θ_(g), θ_(h), are defined as${r = \frac{\sqrt{5} \pm 1}{2}},{\theta_{a} = {\theta_{b} = {\theta_{c} = {\theta_{d} = 0}}}},{\theta_{e} = \frac{3\; \pi}{2}},{\theta_{f} = \frac{\pi}{2}},{\theta_{g} = \pi},{\theta_{h} = 0.}$52. An apparatus for transmitting space-time coded data in a wirelesscommunication system having a plurality of antennas, the methodcomprising: a multiple antenna encoder for combining complex weightswith data symbols and allocating the data symbols combined with complexweights to at least two transmit antennas during at least one specifiedtime slot; and a plurality of antennas for transmitting the data symbolscombined with complex weights to a receiving end via the at least twotransmit antennas during the at least one specified time slot.